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Bivariate Parameter-Objective Function Diagnostic Plot for Hydrological Calibration

plot_2parOF.Rd

Produces a scatter-based diagnostic plot to explore the relationship between two model parameters and a goodness-of-fit (GOF) metric.

This function is particularly useful in hydrological modelling to assess parameter interactions, equifinality, and behavioural regions after calibration or Monte Carlo simulation.

Usage

plot_2parOF(params, gofs, p1.name, p2.name, type="sp", MinMax=c("min","max"), 
            gof.name="GoF", main=paste(gof.name, "Surface"), GOFcuts, 
            colorRamp= colorRampPalette(c("darkred", "red", "orange", "yellow",
            "green", "darkgreen", "cyan")), points.cex=0.7, alpha=0.65, 
            axis.rot=c(0, 0), auto.key=TRUE, key.space= "right")

Arguments

params

A numeric matrix or data.frame containing model parameter sets. Each row represents one simulation.

gofs

A numeric vector containing the goodness-of-fit metric corresponding to each parameter set (in params, and in the same order!).

p1.name

character, name of the 1st parameter to be plotted

p2.name

character, name of the 2nd parameter to be plotted

type

character, type of plot. Valid values are:

-) sp: spatial plot.

-) scatter3d: 3d scatterogram.

MinMax

character, indicates whether the optimum value in gofs corresponds to the minimum or maximum of the objective function. Valid values are in: c('min', 'max').

By default, MinMax='min' which plot particles with lower goodness-of-fit values on top of those with larger values, in each one of the output figures.

gof.name

character, used as the legend title for the goodness-of-fit metric.. It has to correspond to the name of one column of params.

main

character with the title for the plot

GOFcuts

numeric, specifies at which values of the objective function given in gofs the colours of the plot have to change.

If GOFcuts is missing, the interval for colours change are automatically defined by the (unique values of the) five quantiles of gofs, computed by fivenum.

colorRamp

R function defining the colour ramp to be used for colouring the pseudo-3D dotty plots of Parameter Values, OR character representing those colours

points.cex

size of the points to be plotted

alpha

numeric between 0 and 1 representing the transparency level to apply to colorRamp, ‘0’ means fully transparent and ‘1’ means opaque

axis.rot

numeric vector of length 2 representing the angle (in degrees) by which the axis labels are to be rotated, left/bottom and right/top, respectively.

auto.key

logical, indicates whether the legend has to be drawn or not

key.space

character, position of the legend with respect to the plot

Details

This function is designed for post-calibration diagnostics in hydrological modelling workflows. It allows the user to visually inspect how two parameters jointly influence model performance.

When a threshold (GOFcuts) is provided, simulations can be visually separated into behavioural and non-behavioural sets using different levels of performance, which is useful in GLUE-style analyses and uncertainty assessment.

The plot can reveal:

  • Parameter interaction patterns

  • Trade-offs between parameters

  • Regions of acceptable model performance

  • Signs of equifinality

Value

This function only produces a lattice-based figure with the values of the objective function in a two dimensional box, where the boundaries of each parameter are used as axis. It does not return a structured object.

Examples

# Example: Hydrological calibration diagnostic
set.seed(123)

# Generate synthetic parameter sets
n <- 500
params <- data.frame(
  Ksat = runif(n, 1000, 5000),
  Alpha = rnorm(n, mean=100, sd=5)
)

# Simulated goodness-of-fit (e.g., NSE-like)
gofs <- rnorm(n, mean=0.5, sd=0.1)
gofs[1:200] <- rnorm(200, mean=0.9, sd=0.01)

# Plot without threshold
plot_2parOF(params, gofs, p1.name="Ksat", p2.name="Alpha",
            gof.name = "NSE")


# Plot with behavioural threshold
plot_2parOF(params, gofs, p1.name="Ksat", p2.name="Alpha",
            gof.name = "NSE", GOFcuts = c(-10, -0.41, 0.3, 0.7, 1))